Final answer:
The formula to calculate the cross-sectional area of a filament involves rearranging the resistance formula to find A, and then determining its diameter assuming a circular cross-section.
Step-by-step explanation:
To calculate the cross-sectional area A of a filament, we start with the resistance R formula, which is R = (rho * L) / A, where rho is the resistivity of the material, L is the length, and A is the cross-sectional area. Given R and L, and knowing the resistivity rho, we can isolate A to find that A = (rho * L) / R. Once we have the cross-sectional area A, we can determine the diameter d of the filament assuming it has a circular cross-section using the formula A = (pi * d2) / 4, and solving for d will give us the diameter, d = 2 * sqrt(A/pi).